You have a couple of options, depending on how much length is left on the stud.
One is to fold back the carpeting and drill from the inside, and put a new bolt in, being careful to seal the body so there are no exhaust fumes. JB Weld epoxy is good for that. The downside to this is you are drilling blindly, either up or down, so you risk hitting something with the drill bit.
The way I did it was to buy a double-female thread hex standoff, screw it onto the remaining stud, and run a bolt up into it from the bottom. You can find these parts at a hardware store. You just have to know the thread size, which you can get if you take the good nut in and have them gauge it. It's a metric thread, I think it might be M8 x 1.25mm. This repair worked fine.
Be sure to use anti-seize compound on every fastener when you reinstall.
Grind the rest of the bolt down. Pull the back seat out. Go back underneath and drill a hole out where you ground down the bolt. Drop one in from where the rear seat is. Seal it up. I had to do the same on my 89.
I was also able to remove the plate (in my 88) without removing the seats... however - the OP stated 'the car has no interior at the moment'... so if that statement also means - no rear seats are in the car, it will be a bit easier to access - however he plans to tackle the problem
So what do you guys do to keep the bolt from turning when you're doing things up underneath? I've just started on this fix today. I missed when I was drilling, so the hole is just behind the old bolt, but it seems to me that it should work anyway.
If you don't have an assistant, then use a lockwasher before the nut goes on. That way, you can hold the end of the bolt underneath and tighten the nut until the lockwasher contacts the underside of the floorpan and bites in. The bolt will then not turn, and you can tighten the nut.